Page 204 - Percolation Models for Transport in Porous Media With

202 CHAPTER 12. ACOUSTIC WAVES AND PERMEABILITY

capillaries exceed their cross-sections, and therefore characteristic capillary length
is l > w- 6 m.
The presented estimate shows that under acoustic treatment with frequency
within the kilohertz range, the release of energy due to the dissipation during
the directed Bow of a viscous fluid is not observed. Consequently, unlike in the
case of electric action, the effect of localization of the energy release in the thinnest
capillaries, which limit the hydraulic conductivity of the medium, does not appear,
either.

12.2 Destruction of Surface Layer in Pore Chan-

nels under Tangential Stress

When the surface of the pore channels, or at least a part of it, is covered with
a cementing clayey solution drift (or, as in the pre-filter zone of the well, with
mud drift) which has low shear strength, the shear stress developing at the phase
interface during the fluid flow can cause destruction and further hydrodynamic en-
trainment of the solid particles from the boundary layer. Consequently the radius
of the conducting capillaries increases by the value of thickness of the entrained
low-strength boundary layer. This results in the increase of the permeability of
the medium.
Investigate the reality of this effect appearing in the medium, given the char-
acteristic values of the corresponding parameters. Calculate the tangential force
Fr with which the fluid acts on a unit length of a cylindrical circular capillary (89].
From the momentum equation for a liquid cylinder of radius r we have

{12.5)

where 6p is the pressure difference at a distance l. The tangential stress acting
on the surface of the channel by Navier - Stokes law equals
8111 6p r
Ts = -p, 8ro ro=r = -~- 2 (12.6)

The Hagen - Poiseuille formula (12.3) for the profile of velocities for the fluid
in the capillaries was used in deriving the resultant expression (12.6). After ex-
pressing 6pfl in terms of the stress T 8 from (12.6) and substituting the obtained
relation in (12.5), we find the value of the applied tangential force per unit length
of a capillary in the following form

Fr = 211TT8
To obtain the critical value of the shear force, when the removal of the layer
from the surface takes place, we substitute the quantity T 8 with the shear strength